Slepian-type codes on a flat torus

Quotients of IR2 by translation groups are metric spaces known as flat tori. We start from codes which are vertices of closed graphs on a flat torus and, through an identification of these with a 2-dimensional surface in a 3-dimensional sphere in IR4, we show such graph signal sets generate [M, 4] Slepian-type cyclic codes for IM = a(2) + b(2); a, 6 is an element of Z, gcd(a, b) = 1. The cyclic labeling of these codes corresponds to walking step-by-step on a (a, b)-type knot on a flat torus and its performance is better when compared with either the standard M-PSK or any cartesian product of M-1-PSK and M-2-PSK, M1M2 = M.